Chapter 4 Algebra Worksheet Page 19
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501 9 4
C H A P T E R 4 : A L G E B R A
12
Paree is deciding on the size of her garden bed, which is to be rectangular.
Draw a diagram of a rectangle to
a
represent Paree’s garden bed.
If l stands for the length and w
b
stands for the width, label each of the
four sides of the rectangle.
Write an expression for the perimeter
c
of the garden bed by completing this:
l + w +
+
.
Simplify the expression.
d
If P stands for the perimeter, write a formula for the perimeter of a rectangle.
e
f
Use the formula to calculate the perimeter of rectangles with each of these length
and width measurements.
1
1
i
l = 4 m, w = 3 m
ii
l = 6.4 m, w = 2.8 m
iii
l = 15
m, w = 7
m
2
2
g
Paree decides to plant box hedge around the edge of her garden bed. If she has
enough plants to extend around a rectangle with perimeter 20 m, suggest three
different sets of length and width measurements for her garden bed.
13
Consider the expression: 7a + 5b − 2a + 3b + 4a − 6b + c. To simplify this expression,
it is easier to rearrange the expression so that like terms are grouped together. This is
called collecting like terms.
Copy and complete the following
7a − __a + 4a + 5b + __b − __b + c
a
to show how the expression can
like terms
like terms
be rearranged.
Notice that the minus sign (−) in front of 2a has moved with the term. Has this
b
happened with any other term? Explain.
Check that the addition or subtraction sign in front of each term has moved with
c
that term. (That is, does each term still have the same sign in front of it?)
d
Now that like terms have been collected, simplify the expression.
e
Show how you can check your simplifi ed expression is equivalent to the original
expression. (Hint: substitute a value for each of a, b and c.)
Which expression is easier to evaluate if you have a, b and c values? Explain.
f
14
Copy and complete each set of working to simplify the expression.
6x + 4y − 3x + 7y + 5x − 2y + y
a
= 6x −
x +
x + 4y +
y −
y + y
=
x +
y
2mn + 5m + 8mn − 9m + 4n − 6mn + 2m
b
= 2mn +
mn −
mn + 5m −
m +
m +
=
mn −
m +
When rearranging 3x − 2y + 7x − 4y, Tania wrote 3x − 7x + 2y − 4y.
15
Explain her mistake.
a
b
Show how to get the correct result for simplifying 3x − 2y + 7x − 4y.
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